Where is the engine coolant temperature sensor in a 1999 Audi A4 1.6L and how to replace it?

You should have gotten a letter from Audi about an extended warranty. The sensor is now covered for 10 years/100,000 miles for a falty sensor. This sensor (if malfunctioning) will cause the MIL to light up by "sensing" that the engine coolant is a couple degrees above what it should read. No Idea where it is but you shouldn't have to worry about replacing it yourself.